You need to use a short allen wrench, there should be one with the tools that came with the lathe. On mine I bought studs that reach to the back side of the spindle, so you can get a nut and washer on it. You will need to turn 3 bushings that fit in the recessed section hole in the spindle, I made mine so they were flush with the back of the spindle. As mentioned put a witness mark on the spindle and chuck so it goes on the same each time. It takes me less than a minute to remove the chuck now.
Bob